Construction of bi-Frobenius algebras on quiver

Zhan Fa; Yanhua Wang

doi:10.1080/00927872.2025.2605169

Construction of bi-Frobenius algebras on quiver

Zhan Fa
, Yanhua Wang^*

^*Corresponding author for this work

Shanghai University of Finance and Economics
Shanghai Key Laboratory of Financial Information Technology

Research output: Contribution to journal › Article › peer-review

Abstract

Let (Formula presented.) be a basic cycle with n vertices, and let (Formula presented.) be its path algebra. Let J be the ideal generated by all arrows. We constructed the comultiplication and counit on (Formula presented.) so that it acquires the structure of a bi-Frobenius algebra. Moreover, the bi-Frobenius algebra is not a Hopf algebra.

Original language	English
Journal	Communications in Algebra
DOIs	https://doi.org/10.1080/00927872.2025.2605169
Publication status	Accepted/In press - 2026
Externally published	Yes

Keywords

Bi-Frobenius algebras
Frobenius algebras
Hopf algebras
Quiver
path algebras

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10.1080/00927872.2025.2605169

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title = "Construction of bi-Frobenius algebras on quiver",

abstract = "Let (Formula presented.) be a basic cycle with n vertices, and let (Formula presented.) be its path algebra. Let J be the ideal generated by all arrows. We constructed the comultiplication and counit on (Formula presented.) so that it acquires the structure of a bi-Frobenius algebra. Moreover, the bi-Frobenius algebra is not a Hopf algebra.",

keywords = "Bi-Frobenius algebras, Frobenius algebras, Hopf algebras, Quiver, path algebras",

author = "Zhan Fa and Yanhua Wang",

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year = "2026",

doi = "10.1080/00927872.2025.2605169",

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journal = "Communications in Algebra",

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AU - Fa, Zhan

AU - Wang, Yanhua

PY - 2026

Y1 - 2026

N2 - Let (Formula presented.) be a basic cycle with n vertices, and let (Formula presented.) be its path algebra. Let J be the ideal generated by all arrows. We constructed the comultiplication and counit on (Formula presented.) so that it acquires the structure of a bi-Frobenius algebra. Moreover, the bi-Frobenius algebra is not a Hopf algebra.

AB - Let (Formula presented.) be a basic cycle with n vertices, and let (Formula presented.) be its path algebra. Let J be the ideal generated by all arrows. We constructed the comultiplication and counit on (Formula presented.) so that it acquires the structure of a bi-Frobenius algebra. Moreover, the bi-Frobenius algebra is not a Hopf algebra.

KW - Bi-Frobenius algebras

KW - Frobenius algebras

KW - Hopf algebras

KW - Quiver

KW - path algebras

UR - https://www.scopus.com/pages/publications/105028124983

U2 - 10.1080/00927872.2025.2605169

DO - 10.1080/00927872.2025.2605169

M3 - Article

AN - SCOPUS:105028124983

SN - 0092-7872

JO - Communications in Algebra

JF - Communications in Algebra

ER -

Construction of bi-Frobenius algebras on quiver

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